Download a/b Divided by

UNIT 1
“FUNDAMENTALS”
(2 hours of theory and 2 hours of exercises)
Preparatory activities
The teacher will present CLIL to the students
What is CLIL?
CLIL offers opportunities to allow youngsters to use another language naturally, in such a way that
they soon forget about the language and only focus on the learning topic.
It is usually done through putting aside some time in the school week for learning subjects or
special modules through another language. In CLIL the learning of language and other subjects is
mixed in one way or another. This means that in the class there are two main aims, one related to
the subject, topic, or theme, and one linked to the language. This is why CLIL is sometimes called
dual-focussed education.
Imagine learning to play a musical instrument such as a piano without being able to touch the
keyboard. Consider learning football without the opportunity to kick a ball yourself. To learn how
to master a musical instrument, or a football, requires that we gain both knowledge and skill
simultaneously. In other words, we learn effectively by experiencing both learning about the
instrument, and having hands-on practice at using the instrument, at the same time. This is as true
of music and football as of language. (from USING LANGUAGES TO LEARN AND LEARNING TO USE LANGUAGES
David Marsh)
Students will be invited to speak about this CLIL project.
This CLIL unit that deals with Newton’s Laws, is part of the physics plan of the class. It will occur
in the second term of the school year and will last for about 2 hours.
Some Physics concepts used in this topic are part of the curriculum of the first term so it will be
needed to revise the following:

Physics quantities and their units

How to express derived units like m/s or m/s²

Maths operator and its expression

How to express verbally a formula, or a Physics Law

Scalar and vector quantities;

Operations with vectors

Making a graph with Physics quantities

Average velocity and instantaneous velocity

Force as vectorial quantities
Maths and Physics Fundamentals
a/b a divided by b
a/b a upstairs b downstairs
a^2 a squared
a3 a to the power Three
a + b a plus b
a-b a minus b
T delta T
S displacement
> larger
< smaller
0.5
“o point five”
 Plus or minus
= equals or “to find as” or “would be”
Order of magnitude
“the mass has disappeared” (per dire che la massa è stata semplificata in una formula)
I can loose.. (semplificare una variabile)
An object is at rest
To make the assumption (fare l’ipotesi)
To evaluate (calcolare)
Unknown (incognita)
Get smaller or get larger
To take it into account
Concept of Graph or Plot, axis of the Graph, x axis and y axis,
What’s the value of….?
Frame of reference (sistema di riferimento)
Tilt (inclinazione)
Unit of time, unit of mass ecc
Concepts of “convert it to” for instance m/s to km/h
Physics quantities
Length
Time
Mass
Units
meter
second
kg
Concepts of “convert it to” for instance m/s to km/h
This video will help the students to revise the concepts described here above and will introduce
them to the next step (Lezione 1 video 1):
http://www.youtube.com/watch?v=8WThnNzPsvo&feature=player_embedded#!
Vector quantities
If in Italian Physics texts, a vector quantity needs 3 pieces of information to be defined ( magnitude
or size, direction and versus) in English books it only needs 2 (magnitude or size and direction).
A Vector can be shown by an arrow.
Vectors can be “added together” or subtracted “from each other” or a vector can be multiplied by a
scalar.
AB (leggi ei dot bi:) represents the scalar product
AxB (leggi ei cross bi:) represents another vector (we have to call it prodotto vettoriale)
Let’s see and comment on this video together ( Lezione 1 video 2 - about 2.50 minutes).
http://www.youtube.com/watch?v=xJBGfPfE4fQ&feature=player_embedded#at=68
Important kinematic concepts:
distance travelled by an object or “displacement”
time taken to travel a distance
Distance graph: Distance travelled vs. Time
Velocity graph: Velocity vs. (versus) Time
Difference between velocity and speed: we have to know that velocity can be negative or positive
but speed is the absolute value of velocity, so for instance a speed of - 100 m/s is higher than 30
m/s, while for velocity we find the opposite case.
The distance between 2 points is called “separation”
Friction force
This force we have just studied is very important in order to understand Newton’s Laws
This short video will show the students how to face the problem using English language
http://www.youtube.com/watch?v=bWabHxouJW4&feature=player_embedded
Let’s have a look at the English text (Newtonian Physics Benjamin Crowell) digital version free
of charge from www.lightandmatter.com).
Motion with constant velocity.
In order to determine how fast an object is going, you have to measure the time it takes to cover a
given distance; you can get the equation for velocity as
v = x/t
Velocity (v) or speed equals the distance (x) travelled divided by the time (t) it takes to go
that distance.
In example o, an object is moving at constant speed in one direction. We can say this because every
two seconds its position changes by five meters.
In algebra notation, we'd say that the graph of x vs. t shows the same change in position, x = 5.0
m, over each interval of t = 2.0 s. The object's velocity or speed is obtained by calculating
v = x/t = (5.0 m)/(2.0 s) = 2.5 m/s. In graphical terms, the velocity can be interpreted as the slope
of the line. Since the graph is a straight line, it wouldn't have mattered if we'd taken a longer
time interval and calculated v = x/t = (10.0 m)/(4.0 s). The answer would still have been the
same, 2.5 m/s. Note that when we divide a number that has units of meters by another number that
has units of seconds, we get units of meters per second, which can be written m/s. This is another
case where we treat units as if they were algebra symbols, even though they're not.
In example p, the object is moving in the opposite direction: as time progresses, its x coordinate
decreases. We find that t is still positive, but x must be negative.
The slope of the line is therefore negative, and we say that the object has a negative velocity, v
=x/t = (-5.0 m)=(2.0 s) = -2.5 m/s. We've already seen that the plus and minus signs of x values
have the interpretation of telling us which direction the object moved. Since t is always positive,
dividing by t doesn't change the plus or minus sign, and the plus and minus signs of velocities are
to be interpreted in the same way. In graphical terms, a positive slope characterizes a line that goes
up as we go to the right, and a negative slope tells us that the line went down as we went to the
right. x/t = (-5.0 m)=(2.0 s) = -2.5 m/s.
Motion with constant acceleration.
Looking at this graph we can notice that it is no longer true that the object makes the same amount
of progress every second. There is no way to characterize the entire graph by a certain velocity or
slope, because the velocity is different at every moment.
In this case the velocity of an object at any given moment is the slope of the tangent line
through the relevant point on its x - t graph.
Acceleration
Acceleration is the increase of velocity over a period of time. Deceleration is the decrease of
velocity. When you start running, you accelerate (increase your velocity) until you reach a constant
speed.
Mathematically, acceleration is the change in velocity divided by the time for the change
a = (v2 − v1)/(t2 − t1)
where:

v2 − v1 is the end velocity minus the beginning velocity

t2 − t1 is the measured time period between the two velocities
This is often written as a = Δv/Δt, where Δ is the Greek letter delta and stands for difference.
For example, if an object speeds up from a velocity of 240 meters/second to 560 meters/second in a
time period of 10 seconds, the acceleration is (560 - 240)/10 = 320/10 = 32 m/s/s or 32 m/s².
Changing direction can also cause acceleration (or deceleration) because the velocity in that
direction has changed.
http://www.youtube.com/watch?v=zLeqD7cREfw
Exercises (2 hours)
Exercises from A to G from (Newtonian Physics Benjamin Crowell) digital version free of charge
from www.lightandmatter.com).
H What is the average speed of a sprinter who does the 100 m dash in 11.45 seconds?
I. A police car takes off from rest, reaching a speed of 87.7 mph in 2.11 seconds. What is the
average acceleration of the car?
L . A police car takes off from rest with a constant acceleration of 0.007917. How much time does
it take to reach a speed of 76.1 mph?
UNIT 2
(2 hours of theory and 2 hours of exercises)
Newton's First Law
In the previous two lessons we discussed the different ways by which motion can be described
(words, graphs, diagrams, numbers, etc.). This unit (Newton's first Law of Motion) will concern
the ways through which motion can be explained. Isaac Newton (a 17th century scientist) put
forward a variety of laws that explain why objects move (or don't move) and how they do it. These
three laws are known as Newton's three laws of motion. The focus of the first part is Newton's first
law of motion - sometimes referred to as the law of inertia.
Newton's first law of motion is often stated as
an object at rest stays at rest and an object in motion stays in motion with the same speed and
in the same direction unless acted upon by an unbalanced force.
In other words
An object at rest or in uniform motion (at a constant velocity) remains so unless acted upon
by an unbalanced force (net force).
Now we will see this video as far as minute 3.30 (Lezione 2 Video 1)
http://www.youtube.com/watch?v=M_8w-dD4RBE
This allows us to listen to Galileo’s statement and Newton’s statement about the law of Inertia.
Then we will deal with the frame of reference and the conditions for a correct application of the
law of inertia.
But what exactly is meant by the phrase unbalanced force? What is an unbalanced force? In
pursuit of an answer, we will first consider a physics book at rest on a tabletop. There are two forces
acting upon the book. One force - the Earth's gravitational pull - exerts a downward force. The other
force - the push of the table on the book (sometimes referred to as a normal force) - pushes upward
on the book.
There are two parts to this statement - one that predicts the behaviour of stationary objects and the
other that predicts the behaviour of moving objects. The two parts are summarized in the following
diagram.
The behaviour of all objects can be described by saying that objects tend to "keep on doing what
they're doing" (unless acted upon by an unbalanced force). If at rest, they will continue in this same
state of rest. If in motion with an eastward velocity of 5 m/s, they will continue in this same state of
motion (5 m/s, East). If in motion with a leftward velocity of 2 m/s, they will continue in this same
state of motion (2 m/s, left). The state of motion of an object is maintained as long as the object is
not acted upon by an unbalanced force. All objects resist changes in their state of motion - they tend
to "keep on doing what they're doing."
Suppose that you filled a baking dish to the rim with water and walked around an oval track making
an attempt to complete a lap in the least amount of time. The water would have a tendency to spill
from the container during specific locations on the track. The water spilled when:

the container was at rest and you attempted to move it

the container was in motion and you attempted to stop it

the container was moving in one direction and you attempted to change its direction.
The water spills whenever the state of motion of the container is changed. The water resisted this
change in its own state of motion. The water tended to "keep on doing what it was doing." The
container was moved from rest to a high speed at the starting line; the water remained at rest and
spilled onto the table. The container was stopped near the finish line; the water kept moving and
spilled over the leading edge of the container. The container was forced to move in a different
direction to make it around a curve; the water kept moving in the same direction and spilled over its
edge. The behaviour of the water during the lap around the track can be explained by Newton's first
law of motion.
Everyday Applications of Newton's First Law
There are many applications of Newton's first law of motion. Consider some of your experiences in
a car. Have you ever observed the behaviour of coffee in a coffee cup filled to the rim while starting
a car from rest or while bringing a car to rest from a state of motion? Coffee "keeps on doing what it
is doing." When you accelerate a car from rest, the road provides an unbalanced force on the
spinning wheels to push the car forward; yet the coffee (that was at rest) wants to stay at rest. While
the car accelerates forward, the coffee remains in the same position; subsequently, the car
accelerates out from under the coffee and the coffee spills in your lap. On the other hand, when
braking from a state of motion the coffee continues forward with the same speed and in the same
direction, ultimately hitting the windshield or the dash. Coffee in motion stays in motion.
Have you ever experienced inertia (resisting changes in your state of motion) in a car while it is
braking to a stop? The force of the road on the locked wheels provides the unbalanced force to
change the car state of motion, yet there is no unbalanced force to change your own state of motion.
Thus, you continue in motion, sliding along the seat in forward motion. A person in motion stays in
motion with the same speed and in the same direction ... unless acted upon by an unbalanced
force of a seat belt. Yes! Seat belts are used to provide safety for passengers whose motion is
governed by Newton's laws. The seat belt provides the unbalanced force that brings you from a state
of motion to a state of rest. Perhaps you could speculate what would occur when no seat belt is
used.
There are many more applications of Newton's first law of motion. Several applications are listed
below. Perhaps you could think about the law of inertia and provide explanations for each
application.

Blood rushes from your head to your feet while quickly stopping when riding on a
descending elevator.

The head of a hammer can be tightened onto the wooden handle by banging the bottom of
the handle against a hard surface.

A brick is painlessly broken over the hand of a physics teacher by slamming it with a
hammer. (CAUTION: do not attempt this at home!)

To dislodge ketchup from the bottom of a ketchup bottle, it is often turned upside down and
thrusted downward at high speeds and then abruptly halted.

Headrests are placed in cars to prevent whiplash injuries during rear-end collisions.

While riding a skateboard (or wagon or bicycle), you fly forward off the board when hitting
a curb or rock or other object that abruptly halts the motion of the skateboard.
Newton's Second Law
Newton’s first law of motion predicts the behaviour of objects for which all existing forces are
balanced. The first law - sometimes referred to as the law of inertia - states that if the forces acting
upon an object are balanced, then the acceleration of that object will be 0 m/s2. Objects at
equilibrium (the condition in which all forces balance) will not accelerate. According to Newton,
an object will only accelerate if there is a net or unbalanced force acting upon it. The presence of an
unbalanced force will accelerate an object - changing its speed, its direction, or both its speed and
direction.
Newton's second law of motion pertains to the behaviour of objects for which all existing forces are
not balanced. The second law states that the acceleration of an object is dependent upon two
variables - the net force acting upon the object and the mass of the object. The acceleration of an
object depends directly upon the net force acting upon the object, and inversely upon the mass of
the object. As the force acting upon an object is increased, the acceleration of the object is
increased. As the mass of an object is increased, the acceleration of the object is decreased.
Newton's second law of motion can be formally stated as follows:
The acceleration of an object as produced by a net force is directly proportional to the
magnitude of the net force, in the same direction as the net force, and inversely proportional
to the mass of the object.
This verbal statement can be expressed in equation form as follows:

a=

F
m
The above equation is often rearranged to a more familiar form as shown below. The net force is
equated to the product of the mass times the acceleration.

F=

m a
We will now see this video from minute 6.53 to minute 10 (Lezione 2 Video 2)
http://www.youtube.com/watch?v=M_8w-dD4RBE
In this entire discussion, the emphasis has been on the net force. The acceleration is directly
proportional to the net force; the net force equals mass times acceleration; the acceleration in the
same direction as the net force; an acceleration is produced by a net force. The NET FORCE. It is
important to remember this distinction. Do not use the value of merely "any force" in the above
equation. It is the net force that is related to acceleration. The net force is the vector sum of all the
forces. If all the individual forces acting upon an object are known, then the net force can be
determined.
Consistent with the above equation, a unit of force is equal to a unit of mass times a unit of
acceleration. By substituting standard metric units for force, mass, and acceleration into the above
equation, the following unit equivalency can be written.
The definition of the standard metric unit of force is stated by the above equation. One Newton is
defined as the amount of force required to give a 1-kg mass an acceleration of 1 m/s/s.
Test
The Fnet = m • a equation is often used in algebraic problem solving. The table below can be filled
by substituting into the equation and solving for the unknown quantity. Try it yourself and then use
the click on the buttons to view the answers.
Net Force
Mass
Acceleration
(N)
(kg)
(m/s/s)
1.
10
2
2.
20
2
3.
20
4
4.
5.
2
10
5
10
The numerical information in the table above demonstrates some important qualitative relationships
between force, mass, and acceleration. Comparing the values in rows 1 and 2, it can be seen that a
doubling of the net force results in a doubling of the acceleration (if mass is held constant).
Similarly, comparing the values in rows 2 and 4 demonstrates that a halving of the net force results
in a halving of the acceleration (if mass is held constant). Acceleration is directly proportional to net
force.
Furthermore, the qualitative relationship between mass and acceleration can be seen by a
comparison of the numerical values in the above table. Observe from rows 2 and 3 that a doubling
of the mass results in a halving of the acceleration (if force is held constant). And similarly, rows 4
and 5 show that a halving of the mass results in a doubling of the acceleration (if force is held
constant). Acceleration is inversely proportional to mass.
The analysis of the table data illustrates that an equation such as Fnet = m*a can be a guide to
thinking about how a variation in one quantity might affect another quantity. Whatever alteration is
made of the net force, the same change will occur with the acceleration. Double, triple or quadruple
the net force, and the acceleration will do the same. On the other hand, whatever alteration is made
of the mass, the opposite or inverse change will occur with the acceleration. Double, triple or
quadruple the mass, and the acceleration will be one-half, one-third or one-fourth its original value.
Test
As stated above, the direction of the net force is in the same direction as the acceleration. Thus, if
the direction of the acceleration is known, then the direction of the net force is also known.
Consider the two oil drop diagrams below for an acceleration of a car. From the diagram, determine
the direction of the net force that is acting upon the car.
In conclusion, Newton's second law provides the explanation for the behaviour of objects
upon which the forces do not balance. The law states that unbalanced forces cause objects
to accelerate with an acceleration that is directly proportional to the net force and
inversely proportional to the mass.
Gravitational force and the Newton’s second law
Another means of representing the proportionalities is to express the relationships in the form of an
equation using a constant of proportionality. This equation is shown below.
The constant of proportionality (G) in the above equation is known as the universal gravitation
constant. The precise value of G was determined experimentally by Henry Cavendish in the
century after Newton's death. The value of G is found to be
G = 6.673 x 10-11 N m2/kg2
When the units on G are substituted into the equation above and multiplied by m1 (earth mass) and
divided by d2, the result will be g, so an object on the earth will be actracted by a force or in other
words it will have a weight of
F= m  g
The Big Misconception
So what's the big deal? Many people have known Newton's first law since eighth grade (or earlier).
And if prompted with the first few words, most people could probably recite the law word for word.
And what is so terribly difficult about remembering that F = ma? It seems to be a simple algebraic
statement for solving story problems. The big deal however is not the ability to recite the first law
nor to use the second law to solve problems; but rather the ability to understand their meaning and
to believe their implications. While most people know what Newton's laws say, many
people do not know what they mean (or simply do not believe what they mean).
Cognitive scientists (scientists who study how people learn) have shown that physics students come
into physics class with a set of beliefs that they are unwilling (or not easily willing) to discard
despite evidence to the contrary. These beliefs about motion (known as misconceptions) hinder
further learning. The task of overcoming misconceptions involves becoming aware of the
misconceptions, considering alternative conceptions or explanations, making a personal evaluation
of the two competing ideas and adopting a new conception that is more reasonable than the
previously held-misconception. This process involves self-reflection (to ponder your own belief
systems), critical thinking (to analyze the reasonableness of two competing ideas), and evaluation
(to select the most reasonable and harmonious model that explains the world of motion). Selfreflection, critical thinking, and evaluation. While this process may seem terribly complicated, it is
simply a matter of using your noodle (that's your brain).
The most common misconception is one that dates back for ages; it is the idea that sustaining
motion requires a continued force. The misconception has already been discussed in a previous
lesson, but will now be discussed in more detail. This misconception sticks out its ugly head in a
number of different ways and at a number of different times. As your read through the following
discussion, give careful attention to your own belief systems. View physics as a system of thinking
about the world rather than information that can be dumped into your brain without evaluating its
consistency with your own belief systems.
Newton's laws declare loudly that a net force (an unbalanced force) causes an acceleration; the
acceleration is in the same direction as the net force. To test your own belief system, consider the
following question and its answer as seen by clicking the button.
Are You Infected with the Misconception?
Two students are discussing their physics homework prior to class. They are discussing an object
that is being acted upon by two individual forces (both in a vertical direction); the free-body
diagram for the particular object is shown below.
During the discussion, Anna Litical suggests to Noah Formula that the object under discussion
could be moving. In fact, Anna suggests that if friction and air resistance could be ignored (because
of their negligible size), the object could be moving in a horizontal direction. According to Anna, an
object experiencing forces as described above could be experiencing a horizontal motion as
described below.
Noah Formula objects, arguing that the object could not have any horizontal motion if there are
only vertical forces acting upon it. Noah claims that the object must be at rest, perhaps on a table or
floor. After all, says Noah, an object experiencing a balance of forces will be at rest. Who do you
agree with?
(Anna is correct. Noah Formula may know his formulas but he does not know (or does not believe)
Newton's laws. If the forces acting on an object are balanced and the object is in motion, then it will
continue in motion with the same velocity. Remember: forces do not cause motion. Forces cause
accelerations.)
Remember last winter when you went sledding down the hill and across the level surface at the
local park? (Apologies are extended to those who live in warmer winter climates.)
Imagine a the moment that there was no friction along the level surface from point B to point C and
that there was no air resistance to impede your motion. How far would your sled travel? And what
would its motion be like? Most students I've talked to quickly answer: the sled would travel forever
at constant speed. Without friction or air resistance to slow it down, the sled would continue in
motion with the same speed and in the same direction. The forces acting upon the sled from point B
to point C would be the normal force (the snow pushes up on the sled) and the gravity force (see
diagram at right). These forces are balanced and since the sled is already in motion at point B it will
continue in motion with the same speed and direction. So, as in the case of the sled and as in the
case of the object that Noah and Anna are discussing, an object can be moving to the right even if
the only forces acting upon the object are vertical forces. Forces do not cause motion; forces cause
accelerations.
Newton's first law of motion declares that a force is not needed to keep an object in motion. Slide a
book across a table and watch it slide to a rest position. The book in motion on the table top does
not come to a rest position because of the absence of a force; rather it is the presence of a force that force being the force of friction - that brings the book to a rest position. In the absence of a
force of friction, the book would continue in motion with the same speed and direction - forever (or
at least to the end of the table top)! A force is not required to keep a moving book in motion; and a
force is not required to keep a moving sled in motion; and a force is not required to keep any object
horizontally moving object in motion.
Exercises
1. Determine the accelerations that result when a 12 N net force is applied to a 3 kg object and then
to a 6 kg object.
2. A net force of 15 N is exerted on an encyclopedia to cause it to accelerate at a rate of 5 m/s 2.
Determine the mass of the encyclopedia.
3. Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is tripled and the mass is
doubled, then what is the new acceleration of the sled?
4. Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is tripled and the mass is
halved, then what is the new acceleration of the sled?
5 The pulley shown below is weightless and frictionless. The block of mass m1 is on the plane,
inclined at an angle  with the horizontal. The block of mass m2 is connected to m1 by a string.
m1= 100 kg m2= 50 kg = 30 °
a) Assuming there is no friction, calculate the acceleration of the system in terms of m1, m2,  and
g.
b) What condition is required for m1 to go up the incline?
c) Assume that the coefficient of kinetic friction between m1 and the plane is 0.2, m1 = 2 kg, m2 =
2.5 kg and the angle  = 30º. Calculate the acceleration of m1 and m2.
d) What is the maximum value of the friction coefficient so the system can still move.
Before attempting to solve a Second Newton's Law problem like this it is very useful to take into
account the following considerations:
Free Body Diagram.- In every problem where the Second Newton's Law applies it is fundamental
to draw what is called the Free Body Diagram. This diagram must show all the external forces
acting on a body. We isolate the body and the forces due to that strings and surfaces are replaced by
arrows; of course, the friction forces and the force of gravity must be included. If there are several
bodies, a separate diagram should be drawn for each one.
FREE BODY DIAGRAM
- The force that m1 exerts on m2 through the rope has the same magnitude T. This is so because a
rope only changes the direction of a force, not its magnitude assuming a weightless rope.
- The magnitude of the acceleration is the same at both ends of the rope assuming an inextensible
rope.
6 Criticize the following incorrect statement:
If an object is at rest and the total force on it is zero, it stays at rest. There can also be cases where
an object is moving and keeps on moving without having any total force on it, but that can only
happen when there’s no friction, like in outer space.”
Fonti:
http://www.physicsclassroom.com/Class/newtlaws/
http://www.jfinternational.com/ph/second-newton-law-exercises-2.html